
which, upon insertion into (REF ) and use of
tables [1]}, yields the familiar result
for the acoustic field of a ring source [2]}, [3]}, [4]},
\(\mathcal {R}_{n}(K, a, R_{i}, \phi _{i}, \psi _{i})&\approx (-J)^{n}\mathrm {e}^{Jn\psi _{i}}\frac{\mathrm {e}^{JK R_{i}}}{2 R_{i}}J_{n}(Ka\sin \phi _{i}),\) 
